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Monday, January 30, 2012

F comes before M

My subject is the claim I’ve often seen that mathematics is
the source of science and thus the father of modern technologies. A list then
usually follows ending with radio, television, and of late the Internet. Just
last night I read this paragraph in a distinguished book on Mathematics:

However, the
Kantian explanation that we see in nature what our minds predetermine for us to
see does not fully answer the question of why mathematics works. Developments
since Kant’s time such as electromagnetic theory can hardly be endowments of
the human mind or the mind’s organized sensation. Radio and television do not
exist because the mind organized some sensation in accordance with some
internal structure then enabled us to experience radio and television as
consequences of the mind’s conception of how nature must behave.

[Morris Kline, Mathematics, p.
342.]

Sure enough. But the thought here goes astray. It suggests that
mathematics lies behind electromagnetism—and radio and television. No. Faraday
discovered electromagnetism by experiment—before young Maxwell came around to
translate it into elegant mathematical concepts. Thus F came before M. But it
wasn’t Maxwell’s equations that led to radio but more unruly inventiveness by
the likes of Edison, Tesla, Marconi, Morse, and the like; you look in vain for
paeans to math in their histories. Television got itself going in 1884 when a
twenty-three-year old German student named Paul Nipkow punched holes into a
disk; he spun the disk above an illuminated picture and sliced, diced, and
subdivided it into many tiny images that we now call rasters. That was the
beginning.

No. Mathematics is the immensely helpful servant of science—and
technology belongs to the inveterate tinkerers. Later, when inventions come to
be commercialized and engineers get going in rationalizing the processes, each
of them, of course, has had to master calculus and so forth and be handy with
equations—although the results of the most useful of these are in the handbooks
already.

My image is that of two horses harnessed to the same cart.
One is strong and unruly, the other is elegant and spirited. The strong one
does most of the pulling, but when it comes time to take photographs of the
team, people take the picture from the side of the spirited, elegant horse. Oh,
just look at it snort!

There is also a hierarchy here. Math belongs to the upper
classes. Faraday came from a poor working class family and was self-educated (as
an apprentice in a bookshop); he knew very little math; when he rose in stature
and worked as an assistant to Sir Humphry Davy at the Royal Institute, people
there did not consider him a gentleman. Maxwell came from the nobility, his father a lawyer and financially secure. The inventors like to grub about with matter, the mathematicians are more at home
in the airy realms of concepts. Can we do without them? No. But let’s not forget where science really starts.

Finally,
mathematics works because, when successful, it models reality. And reality
works.